Robust Fusion of Irregularly Sampled Data Using Adaptive Normalized Convolution
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Robust Fusion of Irregularly Sampled Data Using Adaptive Normalized Convolution Tuan Q. Pham,1 Lucas J. van Vliet,1 and Klamer Schutte2 1 Quantitative
Imaging Group, Department of Imaging Science and Technology, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, the Netherlands 2 Electro Optics Group, TNO Defence, Security, and Safety, P.O. Box 96864, 2509 JG, the Hague, the Netherlands Received 1 December 2004; Revised 17 May 2005; Accepted 27 May 2005 We present a novel algorithm for image fusion from irregularly sampled data. The method is based on the framework of normalized convolution (NC), in which the local signal is approximated through a projection onto a subspace. The use of polynomial basis functions in this paper makes NC equivalent to a local Taylor series expansion. Unlike the traditional framework, however, the window function of adaptive NC is adapted to local linear structures. This leads to more samples of the same modality being gathered for the analysis, which in turn improves signal-to-noise ratio and reduces diffusion across discontinuities. A robust signal certainty is also adapted to the sample intensities to minimize the influence of outliers. Excellent fusion capability of adaptive NC is demonstrated through an application of super-resolution image reconstruction. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
In digital image processing, continuous signals are often digitized on a regular grid. Data in this form greatly simplifies both hardware design and software analysis. As a result, if an image is available in another format, it is often resampled onto a regular grid before further processing. Super-resolution (SR) reconstruction of shifted images under common space-invariant blur, in particular, reconstructs a high-resolution (HR) image from a set of randomly positioned low-resolution (LR) images. While there are many approaches that achieve SR through an iterative minimization of a criterion function [12, 13, 30], this paper is concerned with SR fusion as a separate step after image registration and before deblurring. A popular method for fusion of irregularly sampled data is surface interpolation. A triangulation-based method [15], for example, first computes a Delaunay tessellation of the data points, then interpolates the data locally within each tile. The triangulation method, aiming to be an exact surface interpolator, is not designed to handle noisy data. It is also expensive to tessellate in achieving SR because of the large number of LR samples involved. Though computationally less expensive, other surface interpolation methods, such as the inverse distance-weighted method and the radial basis function method [1], are all very sensitive to noise. In the presence of noise, a surface fit is often preferred over exact interpolation. A polynomial approximation to a
small neighborhood in the image, known as the facet model, has been proposed by Haralick as early as 1981 [11]. The Haralick facet mode
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